Recently, there has been a growing interest in time-varying photonic media owing to their significant potential in the field of wave manipulation. Here, we explore the exotic characteristics of wave amplification in a photonic time crystal (PTC) made of a spatially homogeneous medium where the refractive index varies periodically in time. Based on qualitative and quantitative analysis of the amplification, we show that the amplification not only depends on the choice of wave vector of a propagating light but also attains different values in different bandgaps. Our approach further extends towards achieving the minimum amount of variation of permittivity required to open momentum gaps to facilitate the phase-dependent amplification of PTCs. Further, we investigate the impact of permittivity variation and choice of number of temporal unit cells to truncate a PTC to mimic the properties of infinite PTC and offer new opportunities to manipulate and control the amplification of light for applications including highly tunable PTC lasers and devices.

中文翻译：

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光子时间晶体的带隙工程和放大

最近，由于时变光子介质在波操纵领域的巨大潜力，人们对时变光子介质越来越感兴趣。在这里，我们探索了由空间均匀介质制成的光子时间晶体（PTC）中波放大的奇异特性，其中折射率随时间周期性变化。基于放大的定性和定量分析，我们表明放大不仅取决于传播光的波矢量的选择，而且在不同的带隙中获得不同的值。我们的方法进一步扩展到实现打开动量间隙所需的最小介电常数变化量，以促进 PTC 的相位相关放大。此外，我们还研究了介电常数变化和选择时间单位单元数量的影响，以截断 PTC 以模拟无限 PTC 的特性，并为包括高度可调 PTC 激光器和设备在内的应用提供操纵和控制光放大的新机会。